Data analysis

Let’s have a first look on how data look like, printing statistics and the original microtubule intensity.

Case Experiment tot min_length max_length average_length
Control 1 22 4.030 13.455 7.859091
Control 2 27 4.225 12.935 7.737407
DM1 1 21 5.395 12.935 8.617143
DM1 2 16 4.355 11.050 7.141875
NF1 1 23 4.875 17.095 8.676087
NF1 2 21 4.030 12.415 6.685714
NF1_DM1 1 20 3.965 12.025 7.520500
NF1_DM1 2 24 3.185 11.245 6.621875

Preprocessing

We computed the Normalized Intensity [0,100] on the signal intensity and then its Rolling Mean (RM) with a window=2, to stabilize the signal.

Tips and body identification

We need to define the body of the microtubule, which can change from experiment to experiment. We can use the tubulin at the extremes of the microtubule: the first and last peak should identify the tips.

For the analysis we considered only the signal coming from the body of the microtubule and considered only microtubules with body length >1.5 microns

## [1] "The following microtubules were removed due to signal length smaller than 2:"
## [1] "Control:MT17:2" "Control:MT19:2" "Control:MT27:2" "NF1_DM1:MT24:2"

Holes identification with adaptive threshold

Now we will identify “adaptive” mean of the microtubule normalized intensity, with an example plot. The analysis first identifies breakpoints (where there is a significant change in the trend), which divide the microtubule in segments. Then we compute a linear model on each segment and consider the coefficient of regression as representative of that segment (blue line in the plot). The maximum between that value and the mean along all the microtubule (green line in the plot) is our threshold to define holes, defined as intervals with intensity below the threshold. To avoid considering holes with a too high intensity, we set the maximum of the threshold to 70% (magenta line in the example plot).

Our main holes will have a minimum length of 0.5 microns.

Holes analysis

How many holes longer than 0.5 microns did we found for each microtubule?

Also, how many holes in general (at least 0.2 microns) and which is their length?

Case Experiment mean min median max
Control 1 2.636364 1 2.5 5
Control 2 2.416667 1 2.0 7
DM1 1 3.809524 2 3.0 8
DM1 2 3.125000 1 2.0 8
NF1 1 3.173913 1 3.0 9
NF1 2 2.666667 1 2.0 6
NF1_DM1 1 3.150000 1 3.0 5
NF1_DM1 2 2.826087 1 3.0 5

Permutation test, n.damages >0.5 microns
Case Experiment mean min median var max
Control 1 2.181818 1 2 0.8225108 4
Control 2 1.625000 1 2 0.4184783 3
DM1 1 2.857143 1 3 1.4285714 6
DM1 2 2.187500 1 2 1.2291667 5
NF1 1 2.391304 1 2 1.4308300 6
NF1 2 1.904762 1 2 0.8904762 4
NF1_DM1 1 2.200000 1 2 1.1157895 4
NF1_DM1 2 2.238095 1 2 0.9904762 5
Comparison pvalue
Control - DM1 3.63e-03
Control - NF1 1.91e-01
Control - NF1+DM1 9.91e-02

Identification of tubulin repair

Let’s start again with a first overview of the tubulin intensity in the microtubules selected by their length.

Case Experiment mean_RMtub_condition sd_RMtub_condition q25_RMtub_condition q50_RMtub_condition q75_RMtub_condition q90_RMtub_condition iqr tmax
Control 1 92.88582 98.98456 47.41280 65.1360 95.5354 168.9250 48.1226 167.7193
Control 2 743.68082 1384.71964 141.91450 198.4100 409.6825 2513.3450 267.7680 811.3345
DM1 1 91.17896 42.33106 60.81040 84.7098 113.7770 146.8688 52.9666 193.2269
DM1 2 146.83122 59.55146 102.56390 132.4796 179.1517 238.8168 76.5878 294.0334
NF1 1 224.42057 278.35838 82.83385 127.7670 240.2929 495.8381 157.4590 476.4815
NF1 2 773.13863 1191.88719 200.52300 342.7340 789.1570 1817.8744 588.6340 1672.1080
NF1_DM1 1 1276.06317 835.59845 700.42300 1068.1990 1633.1255 2243.2480 932.7025 3032.1793
NF1_DM1 2 937.73606 451.56987 647.30000 854.7580 1117.1980 1446.7976 469.8980 1822.0450

Identification of tubulin signal on the tips

We want to identify a threshold for the background tubulin on the Control case, to remove peaks with higher intensity. For each microtubule in the Control, we will find the maximum value on the tips and then compute a distribution. This should describe, in terms of tubulin, the total intensity of the microtubule, and then we can infer a background threshold as 25% of the median value.

Peaks in tubulin intensity

We take the 75th percentile of the tubulin intensity (Rolling Mean with window=2) as minimum height to define peaks (R function findpeaks). To find the peaks we consider a pattern where there are at least 4 increasing and 4 decreasing points. We then remove peaks with height lower than the threshold defined above, to avoid background fluctuations.

We also reduce the width of the peaks by considering the part of the peak lying over the 50th percentile. In this way we can consider only the significant contribution of the tubulin.

Let’s also check for peaks that goes above the 50th percentile, to check if we find something else when NF1 is added. For those peaks the width taken on the 25th percentile.

Analysis

Now let’s analyze the correlation between holes and tubulin peaks. We consider: - the percentage of repaired holes (complete and partial repair) - the percentage of tubulin peaks that are used to repair holes.

Permutation test, repaired damaged sites
Comparison pvalue
Control - DM1 0.0002993
Control - NF1 0.0018306
Control - NF1+DM1 0.0000002
DM1 - NF1+DM1 0.0000000
NF1 - NF1+DM1 0.0208793
Permutation test, not repaired damaged sites
Comparison pvalue
Control - DM1 0.0000023
Control - NF1 0.0323585
Control - NF1+DM1 0.0000007
DM1 - NF1+DM1 0.0000000
NF1 - NF1+DM1 0.0006975

We tested also test the continuous signal of tubulin in the regions where there is a damage vs the regions without damages.

Profile plot for microtubule and tubulin intensity

Let’s now print the profile of the selected microtubules (in purple, continuous line), with the regions that we consider damaged and the tubulin peaks (green continuous line). Additionally:

  • Grey vertical lines define the internal region of the microtubule, used for the analysis.

  • The dotted purple line is the threshold used to define damaged sites, we marked with an * damaged sites with length >0.5 micron.

  • The dotted green line is the threshold to identify tubulin peaks.

Selection of microtubule to plot, as examples, from all the conditions :

  • Control, MT16_2, lev=30;

  • DM1: MT2_2, MT6_1 lev=10;

  • NF1: MT1_2 lev=30;

  • NF1+DM1: MT26_1 lev=30; MT17_1 lev=40